Some classification problems in four-dimensional geometry: distributions, almost complex structures, and generalized Monge–Ampere equations

Three related classification problems on four-manifolds are discussed. First, regular distributions are considered and described locally. After that a classification of almost complex structures of general position in terms of distributions is proposed. Finally, non-degenerate generalized Monge–Ampere equations are classified in terms of $\{e\}$-structures. Symplectic Lie algebras are also considered in an appendix.